Question

sinQ+cosQ=√2 show that sinQ+cosQ=2

Answer 1

I'm assuming Theta (Q) as A.

CosA + SinA = CosA√2
SinA = CosA√2 - CosA   (Take CosA common factor)
SinA = CosA ( √2 - 1) ----> Root sign is only for "2" 
CosA = SinA / ( √2 - 1) ---------------------> (1)

Substituting (1) in CosA - SinA, we get

SinA / ( √2 - 1) - SinA   (take SinA as common factor)
SinA ( 1/( √2 - 1) - 1) -------------> Take LCM
SinA (1 - ( √2 - 1) / ( √2 - 1))
SinA (2 - √2 / ( √2 - 1)) -----------------> Rationalize the denominator
SinA ( (2- √2)( √2 + 1) / ( √2 - 1)( √2 + 1) )
SinA ( (2√2 + 2 - 2 - √2) / 2 - 1)
SinA ( √2 / 1)
= √2 SinA

Hence Proved.

Answer 2

hope my answer helps you